神经网络插值

Question

假设您有这个数据集：

       1.05   1.10   1.15   1.20   1.25  
0.2   0.000  0.000  0.000  0.000  0.000  
0.3   0.350  0.350  0.350  0.350  0.350  
0.4   0.615  0.619  0.623  0.626  0.628  
0.5   0.805  0.816  0.826  0.834  0.839

有没有什么方法可以使用神经网络来插值，例如 0.389 和 1.168，而不仅仅是使用简单插值或双线性插值？

Answer 1

你可以使用

tf.keras.Sequential

:

import os
import random
import numpy as np
import tensorflow as tf

# Set all random seeds for reproducibility on same machine at least.
RANDOM_SEED = 1
os.environ['PYTHONHASHSEED'] = str(RANDOM_SEED)
random.seed(RANDOM_SEED)
np.random.seed(RANDOM_SEED)
tf.random.set_seed(RANDOM_SEED)

# Data
x1 = np.array([1.05, 1.10, 1.15, 1.20, 1.25])
x2 = np.array([0.2, 0.3, 0.4, 0.5])
y = np.array([[0.000, 0.000, 0.000, 0.000, 0.000],
              [0.350, 0.350, 0.350, 0.350, 0.350],
              [0.615, 0.619, 0.623, 0.626, 0.628],
              [0.805, 0.816, 0.826, 0.834, 0.839]])
X1_mesh, X2_mesh = np.meshgrid(x1, x2)
X = np.column_stack((X1_mesh.ravel(), X2_mesh.ravel()))
Y = y.ravel()

# Model
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(64, input_dim=2, activation='relu'))
model.add(tf.keras.layers.Dense(64, activation='relu'))
model.add(tf.keras.layers.Dense(1, activation='linear'))
model.compile(optimizer='adam', loss='mean_squared_error')
model.fit(X, Y, epochs=1000, verbose=0)

# Predict
new_point = np.array([[1.168, 0.389]])
predicted_value = model.predict(new_point)
print(predicted_value)

示例输出：

1/1 [==============================] - 0s 55ms/step
[[0.5972232]]